1. Field of the Invention
This invention relates to semiconductor manufacturing processes. More specifically, the invention relates to a method and an apparatus for computing edge-based proximity correction.
2. Related Art
Dramatic improvements in semiconductor integration densities have largely been achieved because of corresponding improvements in semiconductor manufacturing technologies.
Semiconductor manufacturing technologies typically include a number of processes which involve complex physical and chemical interactions. Since it is almost impossible to find exact analytical formulae to predict the behavior of these complex interactions, researchers typically use statistical models.
Once statistical models are found, they are often used to make corrections to layouts to compensate for undesirable effects of a semiconductor manufacturing process. Note that corrections are typically computed based on nearby features using proximity correction techniques. Furthermore, note that these proximity correction techniques can be used for any semiconductor manufacturing process whose effect can be predicted (or simulated) using statistical models.
For example, optical proximity correction techniques typically compensate for the idiosyncrasies of a lithography process by correcting the feature shapes of a mask. The corrected mask can then be used to generate the desired feature shapes on the wafer.
Present proximity correction techniques typically use linear convolution. In linear convolution, a correction is computed by linearly superimposing contributions from neighboring polygons, wherein a polygon's contribution is typically computed by convolving a statistical model with the polygon. Note that, although linear-convolution based techniques account for the distance of polygons from the evaluation point, they are largely insensitive to the specific positioning of polygons relative to one another.
Unfortunately, the effects of many semiconductor manufacturing processes directly depend on the relative positions of these polygons. Note that, at large feature dimensions, linear-convolution based proximity correction techniques are sufficiently accurate. But, as semiconductor integration densities continue to increase at an exponential rate, it is becoming progressively harder to use linear-convolution based techniques to accurately predict and correct undesirable effects of semiconductor manufacturing processes.
Hence what is needed is an accurate and efficient technique to compute proximity correction for semiconductor manufacturing processes, especially when the proximity effects depend (partially or fully) on the relative positions of polygons.